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        "quote": "它对这三个群而言都是[<u id=\"concept-7-1-adjoint-representation\" class=\"concept-term\" data-concept-reference=\"concepts/lie-theory/adjoint-representation\" data-concept-id=\"concept-7-1-adjoint-representation\" data-concept-identity=\"urn:uuid:0c30dd70-94da-4cce-81b0-03aa524fedef\" data-concept-route=\"/concept-identities#concept-0c30dd70-94da-4cce-81b0-03aa524fedef\">伴随表示(adjoint representation)</u>](../../../../../concepts/lie-theory/adjoint-representation)；对 $\\mathrm{SO}(3)$ 而言，该表示与[<u id=\"concept-7-1-vector-representation\" class=\"concept-term\" data-concept-reference=\"concepts/representation-theory/vector-representation\" data-concept-id=\"concept-7-1-vector-representation\" data-concept-identity=\"urn:uuid:94ff4c93-90de-45ed-a904-70b63d9c30cf\" data-concept-route=\"/concept-identities#concept-94ff4c93-90de-45ed-a904-70b63d9c30cf\">向量表示(vector representation)</u>](../../../../../concepts/representation-theory/vector-representation)同构。<span id=\"source-7-1-quaternion\" class=\"block-anchor\"></span>",
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